Transmissions of COVID19 that occur within the classroom are a key concern for ToscaUniversity administrators, the University community, and the surrounding communities in which they live. The rate of transmission (between students) is expressed in terms of cases (transmissions) per student hour where hour refers to the number of hours a student spends in the classroom. The rate has been estimated to be 1 per 2000 student-

hours. Thus for example a class size of 100, meeting for 1 hour would imply a rate of:

= 1/2000 X 100 students X 1 hour = 0:05

This problem concerns a class size of 118 students that meets for 3 hours per week (assume 100% attendance throughout). We focus first on a 1-week time frame, where the rate can be thought to remain constant. Calculate:

(a) (1 point) The expected value for X

(b) (1 point) The standard deviation for X

(c) (1 point) The coefficient of variation for X

(d) (3 points) The local public health protocol denies an outbreak involving 4 or more transmissions. Calculate the probability of an outbreak if the aforementioned class were to meet for 12 successive weeks (you may assume a constant rate applies across the entire 12 week semester).